Process for the predetermination of the datum values of a wide strip finishing rolling mill train controlled by an electronic calculator

ABSTRACT

A number of improvements are provided in the process of determining the datum values of the rolling mill train. The curvatures of the rolls are continuously determined during the milling run, to take into account wear and thermal expansion. The force to be applied at the final roll-stand to obtain the required strip profile is determined. The power of the rolling mill is distributed between the stands in such a manner that the strip remains plane.

United States Patent [191 Economopoulos et al.

[Ill 3,820,711

[ June 28, 1974 PROCESS FOR THE PREDETERMINATION OF THE DATUM VALUES OF A WIDE-STRIP-FINISHING ROLLING MILL TRAIN CONTROLLED BY AN ELECTRONIC CALCULATOR [76'] Inventors: Mario Economopoulos, 58-Quai de Rome; Stephan Hubert Wilmette, 2 Rue de Chaudfontaine, both of Liege, Belgium [22] Filed: May 1, 1973 [2|] App]. No: 356,130

Related Application Data [63} Continuation-impart of Ser. No. ll5,647, Feb. 16,

l97l, abandoned.

[52] U.S. Cl. 235/I51.l, 72/7 [51] Int. Cl B21b 37/00 [58] Field of Search 235/l5l.l; 72/7 [56] References Cited UNITED STATES PATENTS 3,332,263 7/1967 Beadle et al. 72/7 Primary Examiner Eugene G. Botz Attorney, Agent, or Firm-Holman & Stern 5 7] ABSTRACT A number of improvements are provided in the process of determining the datum values of the rolling mill train. The curvatures of the rolls are continuously determined during the milling run, to take into account Wear and thermal expansion. The force to be applied at the final roll-stand to obtain the required strip profile is determined. The power of the rolling mill is distributed between the stands in such a manner that the strip remains plane.

3 Claims, 7 Drawing Figures A ULA ....h'5-

I EALEULATE NEW EUEFHIIIENTS 71 ..cr6 Q PAIENTEDJUIIZB I974 3,820.71 1

sum 1 [IF 7 9I::HPOWER DISTRIBUTION I H YES I2 32 13 I FIG! IN V E NTOR MARIO EEUNUMIIPOULUS ET AL PATENTEDJUH28 1914 3320.71 1

SE8 2 II: 7

INVENTOR MARIO EEUNUMUiPUULUS ET AL PATENIEIIIUIIZG I874 3; 820.71 1

REDUCE v (VELOCITY) DIAGRAM 0F wAITING HQ 3 PERIOD CHANGE VALUE OF R 57 LINEAR DISTRIBUTION OF T 58 (P='V'7 x 59 B GRAPH 0F CUMULATIVE W- A (TOTAL ELECTRIC POWER) DISTRIBUTION OF W A (TOTAL 60 TMB ELECTRIC POWER) IN MEMORY STORAGE I 6| B---- -'W' I 62 C Pi,

GRAPH OF CUMULATIVE P- (ROLLING FORGE) I (To FIG.4)

wm muuza I974 3,820.71 1

SHEET 5 OF 7 (FROM F|G.4)

H6. 5 w =w l 4 mux. 'L+1 76 H 5 min. 'L+1 77 ex' f f mm. L V k i. max.i, or min.'

8| ALTER VALUE OF P' 82 ELECTRICAL POWER REMAINING TO BE ALLOTTED (DIRECTEM 86 I NEW VALUES FOR P4,P3,P2|

TMB

SHEEI 8 (IF 7 I CALCULATE NEW DISTRIBUTION OF W (TOTAL ELECTRIC POWER) I MODIFY v SER TRAlN 1. 0 ED POSIT V I N6 2. MOTOR SPEED so -ws 3. FORCES P 4. LATERAL GUIDES 5. RING COUPLING moms 6.GAUGE x 7. ROLLING (COILEDI PATH V MEASURE P, I, U, S, N, T ,h

CORRECTION SIGNALS CALCULATE I12. .hg

CALCULATE NEW COEFFIGIENTLI END (OF RUNI 34 MANUAL YES NEW FACTORS NO I PROCESS FOR THE PREDETERMINATION OF THE DATUM VALUES OF A WlDE-STRIP-FINISIIING ROLLING MILL TRAIN CONTROLLED BY AN ELECTRONIC CALCULATOR This is a Continuation-in-Part application of applicants US. Pat. application Ser. No. 1 15,647, filed Feb. 16, 1971, now abandoned in favor of the present application.

The present invention relates to a process for the predetermination of the datum values of a wide-stripfinishing rolling mill train controlled by an electronic calculator.

The endeavour to improve the efficiency of rolling mills, in respect of their production as well as of the quality of the rolled products they provide, has induced the users for some years past to equip their plants with automatic control devices, intended in particular to render it possible to obtain a product of definite constant thickness.

The thickness of gauge control devices in actual use represent solutions developed by the makers and users for optimum compliance with the frequently contradictory requirements corresponding to many and varied demands and conditions. This is the case in particular if it is intended to obtain rolled products whose very first lengths possess dimensions corresponding to requirements.

these dimensions consists in predetermining particular datum values, such as the position of the control screw of the positioning of the rolls of each stand, the speed of rotation of each working roll, and the power to be allocated to eachstand. a H MW Different processes have already been developed for this purpose, among which it is possible to cite those according to which, on the basis of the characteristics required for the strip (gauge, width, exit temperature), power distribution coefficients are selected for the rolling mill frames, from a set of typical distribution factors stored in an appropriate calculator or computer. These coefficients are most frequently determined for a normal production, based on the rolling mill operators experience.

A method of this kind nevertheless has a number of disadvantages, among which it is possible .to cite the impossibility of making allowance for protracted stoppages of the train, or for its particular or accidental conditions (eg pronounced wear of one of the rolls); the necessary limitation in the possibility of adaptation of the said coefficients due to the fact that the modifications to be applied are obtained as differences from the datum values attributed to the preceding strip; the difficulty of finding a distribution resulting in the production of a satisfactory plane strip, among the different typical distribution sequences stored. As a matter of fact, it must be observed that this process makes but little provision for the planeity of the strip; and the impossibility of verifying the transverse profile of the strip.

The present invention will now be described in more detail, by way of example only, with reference to the accompanying drawings, in which:

FIGS. 1 and law consecutive drawings of a block diagram illustrating a process according to the invention;

A well-known method playing a part in maintaining FIGS. 3 to 6 are consecutive drawings of a block diagram illustrating a more detailed flow sheet of a modified process according to the invention; and

FIG. 7 is a schematic of a rolling mill indicating schematically the data stored in a memory unit.

Before defining the different stages of the process of the invention, a sequence of operations which according to a known method results in the determination of the datum values of a six-stand finishing-train, will be described by way of example; the modifications made in this sequence for adaptation to the process of the invention, will be described thereafter. FIGS. 1 and 2, whose drawings are consecutive, illustrate a complete sequence of the operations performed according to a known process, with a sequence corresponding to the process of the invention. The successive stages of the processes are numbered serially,

1. As soon as the strip to be rolled leaves the roughing train to pass into the finishing train, a subprogram (denoted by TCK) operating in conjunction with devices for detection of the position of the strip, is put into operation (start) and, in addition to the position of the slab, supplies the number identifying the slab to be rolled. v

2. The slab number is identified ina drum-type storage unit (TMB) of the electronic computer controlling the rolling mill, which renders it possible to ascertain the quality of the steel k; the gauge h required at the exit of the last (sixth) roll-stand; the temperature T required at the exit of the last rollstand; and the temperature T required upon coilmg.

3. The memory drum unit also supplies the values D of the diameters of the working rolls of the six stands.

4. The thickness h the temperature T and the Width B of the blank at the exit of the roughing pass train, are measured by means of a subprogram- (denoted by DTL) linked to a set of measuring instruments.

5. The value of the speed V at the exit of the finishing train is determined by means of a known thermal model A (for example predetermined graphs), as a function of the temperature T, and gauge k Alternatives are conceivable; at a predetermined point of the sequence use is made of some model (generally detennined from theoretical considerations or experimental date), which provides the value or values of a definite parameter, permitting calculations and operations of the sequence.

MODEL A A simplified model giving the temperature T of the sheet at runout from the train in function of:

the run in temperature T, in the finishing train the run out speed V of the sheet the run out thickness h of the sheet the run in thickness 11 of the sheet. This relationship takes the form: T a T a V h a h, a a formula where a,, a a a, are coefficients determined by the statistical analysis of the measurements T V h h made on the train. It will be observed that this relationship can obviously be written in the form 1 f( E7, v)

which permits to use model A for calculating either T or V,.

6. The flow of material d) per unit of width, 4) V -h is deduced therefrom.

7. The reduction in thickness r,, to be performed in the last roll-stand is selected in the memory unit (TMB) of the computer. This selection is made on the basis of the characteristics of the strip (that is to say, in particular, its thickness h, and its width B). These different values of r are fed into the memory unit once and for all time; they are the result of the rolling mill operators experience.

8. Knowing h, and r,,, it is possible to determine the entrance thickness h,, at the last roll-stand.

9. Among the various typical distributions of power between the six roll-stands, stored in the memory unit TMB, that which corresponds best to the characteristics of the strip is selected. Here again, the data are empirical and may be modified by the rolling mill operator.

' 10. The total rolling power, obtained from an appropriate model B supplying the total power absorbed by the rolling mill train, as a function of factors such as (b, I1 T k, is distributed according to the typical distribution selected in step 9; the powers W, W developed at the first five stands, the power W needed at the sixth stand being determined moreover from h,, r,,, V,, k, are thus known.

MODEL B (b V7 X h1 the width B of the sheet the hardness of the steel k the temperature T,- of the sheet at the i-th stand. This model is given by the formula:

with TB,- 860 (TB, 860) (6 [/5).

TB, and C are two constants depending on the class of final thickness h, and obtained statistically. Th germ class" is synonymous of category. KG and KT are two constants depending on the class of hardness of the steel k and are obtained statistically. T, is the value obtained for the temperature of the sheet at the i-th standard. This value is determined from the initial hypothesis that the said temperature varies linearly between the run in and run out of the sheet in the finishing train. It will thus be with obvious notation:

T.- =T6 (T. T.) (6 i/s).

This is the value used to initiate the calculation; it will ultimately vary, as will, incidentally, all the other values, as the calculation as a whole is iterative.

The value of the tenn (KG) hardness of metal is adapted in the course of rolling a series of coils of the same theoretical hardness. When the measurements are available, the measures values and the provided values of the total power are compared. The value of the coeificient KG which would have given the same total power as the measured value for the same final speed is defined:

" ictiliid m measured (l) flow of material in the train. The value of KG in memory is modified according to the formula:

KG KG 'y (KG KG).

Fig. 1

is clearly the total electric power that is to be spread between the various strands. This graph may be used more particularly to determine by linear interpolation the sheet thicknesses between the stands (rolls) from a particular distribution of power between the stands. (It is then implicitly assumed that the cumulative power curve remains unchanged if the scheme of reduction is altered.)

l 1. A check is made as to whether any of the power W,- exceeds the maximum permissible power W should this be the case, the operative is notified by a warning signal (alarm) and takes any steps considered to be appropriate.

12. The thicknesses h, 11 h.,, h, of the strip between the various stands are determined. by means of the model B. h,,- is known, as well as the power allocated to the fifth stand, which renders it possible to determine h then h.,, h, by means of a progressive analogous calculation.

13. Based on the law of flow conservation (4: constant), the linear speeds V, V of the strip are calculated, beginning with V, h, V, h,,, etc. After the reductions r, r r (r,- (h, h,) h,- have been calculated, the values of the forward strips g, g,, are determined (g, is a known single-valued function of r,). The peripheral speeds of the working rolls N, N, are known from the formula:

Knowing the diameters D of the working rolls, it is then possible to establish the datum values of the angular speeds of the motors driving them.

14. The values of the forces P,- exerted at the six stands are determined on the basis of a predetermined model C (giving P, as a function of 12,-, (11, T k, etc.).

MODEL C z= Pi/B- ewrot 1A1) The two variables x and y are defined by the following relationships:

representing expressions of the type appearing in the process of calculating P,- from the data.

By analogy with the preceding model it is possible to construct the graph of cumulative forces starting from that of cumulative powers, for (cf. FIG. 1) if W, are known 12, and h, h are obtained, and from model C one obtains P,-. It is thus possible to obtain a graph, such as the following (FIG. 2).

l l/hs... ,1/ 4 The significance of this graph will become apparent later on.

ADAPTATION OF THE FORCE MODEL Table Z F(X, Y) The adaptation process consists in modifying the val- An equivalent expression exists for 2' 2' and Z'.,.

15. A check is made to ascertain whether the total permissible force has been exceeded, and the operative is notified by a warning; signal (alarm) if this is the case. I

16. The datum values s s for the position of the clamping screws are then calculated on the basis of a model D (for example; s, =11, (P /M where M,

is the modulus of rigidity of the stand under consideration).

MODEL D A mathematical model used to calculate the position of the clamping screws S,- in function of:

the run out thickness h the speed V,-

the width of the sheet B the cambers of the working rolls [2, and support rolls b,,,. The following formula is used:

where f,, f f;, are functions determined by appropriate measurements carried out on the stand in question, m" is a specific constant found experimentally, M is the yield modulus of the stand in question.

17. The datum values to be applied to the motors driving the loop tensioners are defined in the mem- .ory unit TMB on the basis of the characteristics of the strip (empirical data known beforehand).

18. At this stage, it is possible to control the positioning of all the servomechanisms of the train on the basis of their datum values 1. of the positions of the clamping screws (s;),

2. of the speeds of the driving motors (N 3. of the forces at the automatic gauge control devices (P 4. of the position of the lateral guides,

5. of the torque and position of the loop tensioners,

6. of reference to the X-ray gauge (thickness gauge), and 7. of the speed of the intake rollers. The strip can enter the first roll-stand at this moment.

19. As soon as the strip enters the first stand, a measurement is taken of the force P 20. The result of the measurement of P is compared with the predicted value; the value P (called reference or calculated) is that determined by means of Model C above. If the error exceeds a given value,

an appropriate correction ismade in respect of the position of the screws of the five following frames, in such manner as to make the predicted value equal to that measured. If a difference is found (excess or defect) between the calculated and measured value of P, the values of P,- and S,- of the other stands are suitably modified so as to preserve the same run out thickness of the sheet. The sense of modification of the P, and S,- is well determined (for instance, if the measured P, is less than the calculated P the values of the following P,- are reduced and the corresponding S,- are corrected so as to reduce the P The same procedure may be applied in respect of the second stand. A period of sufficient length to be able to perform corrections based on measurements made at the following stands is most frequently unavailable.

21. A series of data is measured during passage of the strip; rolling forces, positions of the screws, motor currents and voltages (to obtain W positions of the screws, motor speeds, exit temperature, and exit thickness.

22. The values of the strip thicknesses h h between the frames are then calculated from the equation (1) C' and from the measurements of N, and h,.

23. From these recalculated values are determined new values of the parameters intervening in the models B and C, which are then re-inserted into the memory unit of the computer, thus rendering it possible to apply a permanent adaptive control of the rolling process.

The modifications and improvements introduced in the process itemised in l to 23 above, relate in particular to the method of distributing the power of the rolling mill between the stands (except for the last stand, in which a specified reduction is performed). In the above known conventional sequence, a selection is made from a set of coefficients stored in the memory unit of a computer, of those applicable to a strip whose characteristics correspond most closely to those of the strip to be rolled. These coefficients are determined for a normal production run, based on the experience of the rolling mill operator. As described in the foregoing, this method has the short-comings already cited above.

The improvements forming the object of the present invention, have as their object to control the operation of the train in such manner as to obtain a plane strip having the required profile 2 These improvements are based on:

a the continuous determination of the curvatures of the rolls during a mill run. The curvatures in question correspond to the longitudinal profile of the rolls. A model F indicates the manner in which they are affected by wear, and a thermal model E indicates the manner in which they-are affected by thermal expansion of the rolls; these models consist, for example, of graphs, formulae, or measuring pickups.-

MODEL E A mathematical model used to calculate the development of the camber of working rolls in function of their thermal condition, as a function of:

the thickness of the sheet at run in and run out,

the rolling force,

the temperature of the sheet in the stand,

the speed,

the width of the sheet,

the rolling time,

the duration of the interval between sheets. To construct model E use is made of certain simplifying hypotheses, intended to facilitate calculation.

Thus, it is known, for instance, that a given point on the perimeter of the roll may in the course of a complete revolution of the roll find itself in successive contact with water at high pressure, with trickling water, the support roll, and the sheet. For the purpose of simplification this complex external ambience is assimilated to an equivalent homogeneous ambience, i.e., one exchanging the same total quantity of heat with the roll; this equivalent ambience will have an equivalent temperature V and an equivalent transfer coefficient g.

It may then be assumed that the flow of heat across the surface of the roll is given by 1J=g (T V), a formula in which T is equal to the temperature of the roll at the point in question. The problem is thus reduced, by reason of radial symmetry, to working out a two dimensional model for calculating the thermal evolution of the roll. The distribution of temperature in the roll is obtained by solving by the method of finite differentials the well-known equation of propagation of heat described in cylindrical co-ordinates. This solution, trite as it is, supplies the instantaneous values of temperature at any point of the roll. From the thermal field thus established one calculates the values of surface displacements on the roll in an approximate manner by assuming that the roll is cut up into a certain number of sections, and that every section of the roll is deformed independently from the adjacent sections. The displacements on the surface of the roll being known, it is possible to determine the camber from the difference between the diameter measured at the the center of the rolls length and the diameter measured at one of the two ends of the working surface of the roll.

b. The determination of the force to be applied at the sixth stand to obtain the required strip profile (accordingly, it is the force which is imposed, and not the reduction as in the known process).

0. The distribution of the power of the rolling mill between the stands in such manner that the strip remains plane; this condition may be demonstrated in the following manner: the relative difference between the profile of the strip at the entrance and exit of the stand (the planeity coefficient) should remain smaller than a definite limiting value, referred to as a critical value. This condition may be described in the form:

where d) planeity coefficient (or relative difference),

2,, profile of the strip at the entrance,

2, profile of the strip at the exit, and

crit critical planeity. coefficient (experimental function of the dimensions, temperature, and nature of the steel).

In the case in which several distributions appear to be possible, that which results in the most uniform power distribution between the different stands will preferably be adopted.

, Referring, at this juncture, to the schedule 1-23 (FIGS. 1 and 2) already described, the improvements brought about by the invention may be itemised as follows:

24. The transversal profile E must be added to the characteristics required at the exit point.

25. From thermal model E of the roll curvature, the

' momentary values of the curvatures are calculated, with allowance for the heating of the rolls during the passage of the preceding strips, and for their cooling during the period in which there is no strip being rolled.

26. These values are corrected to make allowance for wear, by employing an appropriate model F or sensor.

MODEL F A model used to described the progressive wear of the working roll. This model is very simple; it is based solely on two hypotheses:

wear is suffered only by the part of the roll in contact with the sheet;

the amount of wear is proportional to the length of the sheet being rolled. This wear is, therefore, formulated by U 'T k L k k, and k being specific constants of the'case in question. The true curvatures of the rolls are thus obtained at any time, in particular at the instant at which the strip is about to penetrate into the various stands.

27. The force P to be applied to the sixth stand is calculated by employing a model G indicating the profile of the strip as a function of the parameters of the pass (k 8,0 etc.).

28. The thickness of the strip at the entrance to the last stand is then determined from the model C. We are thus referred back to operation 9 of the initial schedule.

it is then apt to check whether the power distribution found as a first approximation results in the production of a plane strip.

29. Knowing the curvatures of the rolls, the forces P applied at all the stands, and the strip thicknesses between the stands, it is possible to calculate the profiles of the strip at the exits of the various stands 2, 2 from a model G.

MODEL G A mathematical model used to calculate the crosssectional profile E i+ l of the sheet at the run out from a stand in function of:

the length L of the table, the thickness h the force P the width B of the sheet, the diameter of the working rolls DW, and support l'OllS D the cambers of the working and support rolls 0', and

0A,. The relationship which is used reads as follows:

a formula where f(h, h

a, to (1 and specific coefficients determined statistically as above. 30. The values of the planeity indices at all the stands are determined from formula (1).

31. A check is made to establish that the critical values of the planeity index have not been exceeded at any stand. These values are calculated on the basis of an appropriate model. H. If this is the case, the calculation is continued as in operation 16.

MODEL H This model permits to define a criterion of flatness of the sheet at run out from a stand. It may be written in the form 32. If not, in operation 9, the distribution of power between the frames is modified by means of an appropriate algorithm, and the coefficients contained in the memory unit are adapted accordingly. The calculation is then resumed as in operation 10 with this new distribution, until all the satisfactory values are obtained for the P," 33. As soon as the strip leaves the stand, all the d, are recalculated from model B, and they are applied for recalculation of the 0,- employed in operation ,25.

34. If manual intervention has been performed, the values of the coefficients in the memory unit are corrected in such manner that allowance is made for the corrections made by the rolling mill operator, during the predetermination of the datum values for the following slab.

According to a different form (FIGS. 3 to 6) of the modifications introduced by the process of the invention in the known process, the determination of the datum values of the rolling mill train is performed by the following successive operations:

1 4: list of data (unchanged from that already mentioned above) 3 (D diameter of the support roll in question) 5-25z first estimate of the speed of the sheet at runout from the finisher and constructing the cumulative graphs of force and power 5 the maximum speed the head of the sheet can attain is calculated. This speed is the lowest of the following boundary values:

speed as at the end of acceleration, the speed does not exceed the boundary speed of the motors;

speed as at the end of acceleration, the power does not exceed the boundary power of the motor at the most highly loaded stand;

maximum engagement speed at the coils;

such a speed that the intended temperature of the windings can be obtained over the whole length of the neck of the coil.

52 A certain percentage of this boundary value (for example a 0.9) is taken as the starting value for the speed.

53 The temperature T of the sheet at the runout from the train is calculated by means of a simplified thermal model A. v

54 The obtained value T is compared to the envisaged value T 55 If the calculated temperature is too high the speed is reduced and if necessary the time which the bar has to spend before the descaler is computed.

56 If the calculated temperature falls short of the envisaged temperature by an amount exceeding b (e.g. b C), the instructed thickness value is altered (e.g. this value is increased by the tolerance in function of the production requirements; in fact, this may be a matter of re-assignment to a different class).

57 The temperature of the sheet at each stand is computed on the assumption of linear distribution of temperature between the runin to the stand (roll) 1 and runout from the stand 6. In fact, the first cycle of the calculation must start off from some fairly plausible hypothesis. The true temperatures will be determined progressively in the subsequent cycles of the calculation, as the general method is iterative (ex. No.64).

58 The flow of material per unit width is equal to 59 The graph of cumulative power is constructed for the base thicknesses (model B).

60 The power distribution corresponding to the thickness class and the width class of the rolled products is selected from the computer memory.

6] The power is distibuted among the stands according to this distribution and the thickness values between the stands are determined (model B).

62 The forces P,- at each stand are calculated from model C.

63 The graph of cumulative forces is constructed.

64 The values of the temperature at each stand (roll) and at the runout from the finisher are computed from the mathematical model I, which gives the evolution of temperature of the sheet in the finisher.

65 The latter values is compared with the reference value. If the difference exceeds a certain figure the value of the speed V is corrected.

MODEL I A model allowing to calculate the development of the temperature of the sheet in the finishing train.

a. outside the stands the development of the mean temperature T over the thickness of the sheet may be described by the relationship.

a formula h thickness of the sheet I a diffusivity of the sheet k conductivity of the sheet. b. inside the stands heat exchanges are determined by means of the two following relationships: rise in temperature by the work of deformation TM M (a/k) [e/B un-( i i+1) 1 1n t/ m) cooling by contact with the roll ATH- a [L- .s hi h...) 1- V R... (h.

)/V,] formulae'wherein coeffi oients determiiied by the statistical analysis of the measurements made on the train (T h R whence it is deduced: Temperature at run out from a stand Temperature at run in into the same stand AT, AT,.,-. The calculation of the various temperatures can thus be continued by successive approximation.

ADAPTATION OF THE TEMPERATURE MODEL The fall in temperature between the exit of the roughing train and the exit of the finishing train is given approximately by the following expression:

. AT 1 8i h m are characteristics functions of the strip; g,- are the transfer coefficients. Each time a set of measurements is carried out, the

best approximations of the value of the coefficients g, are calculated by using the formula:

8' g. v vii/2.- m 2 KAT) AT] (AT),,, is the measured value of the fall in temperature.

25-27 Calculating the actual values of the cambers.

25 The instantaneous values of the cambers, taking the heating into account, are calculated from the thermal model of the camber E.

26 The instantaneous values of the wear of the rolls are computed from model F; the wear profile is thus determined, which enables the real profile of the rolls'and to this extent their real camber to be obtained by the simple addition of the thermal profile determined in 25. 27 9- Calculating the rolling parameters of the stands 6 and 5. r 2 7 The force P that isto be applied at the last stand to obtain the desired profileE, is calculated by using a model G giving the profile of the sheet in function of the pass parameters.

28 The run in thickness at the sixth roll (stand) is found on the graph of cumulative forces. The speed at run out from stand is given by V (b/h 66 The corresponding power is of cumulative power.

67 In order to achieve the most advantageous conditions so far as flatness at the stand 6 is concerned, the condition is imposed that the run in profile shall be equal to the run out profile: E Z

68 The force at stand 5 that allows to obtain this profile is calculated from the profile model G.

69 The runin thickness at stand 5 is found on the graph of cumulative force.

The run out speed at stand 4 is likewise calculated.

7O The power at stand 5 is found on the cumulative power graph.

71 The value of the sums of forces and powers to be distributed between the four first rolls (stands) are calculated.

These values aretaken straight from the cumulative graphs. i

72 These values are compared with the boundary values of the quantities to be distributed. If these boundaries are exceeded the envisaged value of the run out profile E is altered.

9-51 Calculating the rolling parameters of the stands 4, 3, 2, and l.

The first part of the calculations is common to the stands 4, 3 and 3 (982).

9 Initial steps (assigning calculating parameters successively to every stand, from 4 to 1).

73 The residue of power is equally distributed between the stands that have not yet been taken into consideration.

74 The run in thickness at the stand is calculated from the cumulative power graph.

75 The corresponding force is found on the cumulative force graph. I

7.6 The. extreme values between which the profile at run out from the stand must lie for the sheet to be flat when leaving the next roll (stand) are calculated by making use of the flatness model H.

87 New values are calculated for the thicknesses and the powers on the cumulative graphs, as well as new values for the speeds.

88 New values of the coefficients of power distribution are determined and fed into the memory of the ordinator.

, 51-16 Recalculation of the exit temperature.

51 The values of the temperatures ateach stand (TE,) are calculated as well as at the exit of the mill found on the graph.v

(Ta), making use of the thermal model 1. The difference T between the desired value T and the calculated value T is determined.

52 If this difference exceeds the allowed difference, a correction in the speed V is effected, and the cal culation is resumed in 57. If this difference does not exceed the allowed difference, the calculation is pursued in 16;

16-23 As above.

The initial distribution of the loads between the stands (60) can be modified on the introduction of restrictions of profile and planity. This is why this distribution is recalculated in order, if desired, to be used in place of the above in the event of looping (89 57). This method of procedure speeds up the convergence of the calculation. The calculation of the new distribution consists solely in recalculating the values of or, (Wt/2W by using the values of W, which have just been calculated for each stand.

On the basis of the measured values of the speeds at each stand and of the measured value of the thickness at the outlet of the mill, the corresponding values of the thicknesses at the outlet of the other stands are determined.

77 The corresponding boundary forces are determined from the profile model G. As the upper limit of the force is taken the smaller of the two found values by comparing the value corresponding to the maximum profile with the value of the admissible force at the heat of the sheet.

78 If the value of the force found in does not fall within the limits, it is taken to be equalto the near est limit. i i

79 The new value of the run in thickness is calculated on the graph of cumulative force and of the run in speed.

8O The new value of the power is found on the cumulative power graph. I

81 A test is made to see if the boundary values of. power and speed are exceeded. If this be so, the value of the force is modified, provided that it does not exceed the admissible value.

82 The residual power is determined and the calculation is resumed for the precedingstand, i.e., 3, then stand 2. t g

83 The calculations are started for the stand 1 by determiningthe value of the force corresponding to the maximum reduction.

84 The ratio is determined between the force that remains to be imparted to the stand 1 and the boundary value.

85 If this ratio exceeds 1 by an amount greater than C 1 (value found in practice) the value of the run out profile is increased, so as to give a higher force to the last stands, and the calculation is resumed at 27. i

86 If this ratio exceeds 1 by an amount smaller than C l a correction is made to the forces calculated for the stands 4, 3 and 2 so as to make the residual force for the stand 1 at most equal to the boundary value.

These values can be different from those provided by the calculation. In order to make 'this'calculation, the

conservation equation of the flow of material in the train (58) is used.

As a function of the difference between the calculated values and the measured values of the powers, forces and temperatures, the coefficients of the models used are adapted to calculate these different magnitudes. It is these adapted models which will be used during calculations for the following strip:

power adaptation: the adaptation bears on the term relative to the hardness KG;

force adaptation: the adaptation bears on the values in the table surrounding the point corresponding to the measured value;

Temperature adaptation: The adaptation bears on the values of the transfer coefficients between stands (g).

Someschedules representing operational sequences according to the process of the invention now having been described, the essential features thereof are defined in the following.

The process forming the object of the present invention, relating to the predetermination of the datum values of afinishing rolling mill train for wide strip, controlled by a computer, in which data are imposed, such as: the thickness of the strip at the egress point from the last frame of the rolling mill; the temperature of the strip at the egress point from the rolling mill; (see model I below); the required temperature of the strip at the coiler, in which are specified: the nature of the steel of the strip; the diameters of the working cylinders, in which measurements are made, such as: the width of the strip; the temperature of the strip; the thickness of the strip. These three measurements being taken at the point of egress from the roughing pass train, and wherein the speed of the strip at the egress point from the rolling mill is determined by means of mathematical pattern, and/or charts, which are known per se, is essentially characterised in that, in particular whilst employing automatic devices, mathematical patterns charts and sensors, the following operations are performed, the value of the profile of the strip at the egress point from the rolling mill being imposed moreover; the momentary values of the curvature of the cylinders are determined, taking account of their attrition and of their thermal condition; the force to be applied to the last frame is determined; the thickness of the strip at the ingress point to the last frame is determined; for example, among typical distribution sequences for division of power between the different frames, said distributions being stored in a computer memory unit, that is selected which corresponds best to the characteristics of the strip; the total power absorbed by the rolling mill is divided according to the distibution selected, and a check is made to ascertain that'the power of each frame does not exceed a given maximum; the thicknesses of the strip between the different frames, the linear strip speeds, the corresponding reductions and slips, and finally the peripheral speeds of the working cylinders, and the datum values of the angular speeds of the driving motors of these cylinders, are determined consecutively; the forces exerted in the rolling mill frames are calculated, a check being made to ascertain whether these forces exceed a given maximum value; a check is made to ascertain whether the distribution of the forces found hereinabove renders it possible to produce a plane strip, preferably in the following manner: the profiles of the strips at the egress points from the different frames, are calculated; a planity coefficient is calculated for each frame from a formula of the nature of that marked (1) and a check is made to ascertain that this coefficient remains smaller than a given critical value; if the condition above is not fulfilled, an appropriate algorithm is employed to modify the law of distribution of the between the frames, the new corresponding values of the planeity coefficients are calculated, until they are all smaller than their corresponding critical value; the following consecutive operations are then performed: determination of the datum values of the positioning of the clamping screws and of the forces at the automatic thickness or gauge control devices; selection of the datum values for the loop tensioner devices infeed of all the datum values into the corresponding servomechanisms.

Once all the datum values have been fed-into the corresponding servomechanisms, the strip is fed into the rolling mill, and particularly on the basis of measurements taken on the strip in process of being rolled, or on one or another apparatus of the rolling mill, it is possible according to a process known per se, to modify one or more of the parameters conditioning the operation of the rolling mill, in such manner as to reduce any difference possibly detected between the datum values fed in and the corresponding measured or observed values or to make allowance for all the modifications wrought in the said parameters by a manual intervention of the operative.

According to an advantageous version of the process described in the foregoing, the determination of the thickness of the strip at the ingress point to the last frame is followed by the following consecutive operations: selection of a division of the forces to be applied to the different frames, for example from a set of typical divisions stored in the memory unit of the computer; determination of the forces to be applied to all the frames of the rolling mill, except for the output frame, and verification of whether these forces exceed a definite maximum value; determination of the different thicknesses of the strip; determination of the datum values for the positioning of the clamping screws; feed of the datum values for the screw clamping action and for the forces applied at the frames, into the corresponding servomechanisms; determination of the profiles of the strip between the different frames; determination of planeity indices, for example by means of the formula (1), of the critical values of these indices, and comparison with each other; in case of an insufficient value of one of these indices, two kinds of correction are introduced into the memory unit (the one relating to the thickness of the strip, the other to the forces applied) to modify the division selected for the forces applied to the frames, and the calculation is carried on again until all the planeity indices are smaller than their corresponding critical vlue; the reductions, the linear speeds of the strips, the slips, the circumferential speeds of the working cylinders, are then determined; the datum values for the speeds of the motors are fed into the corresponding servomechanisms; the power absorbed by each frame is determined, and it is verified that these powers remain smaller than a given maximum value; a search of the memory unit is made and the datum values applicable to the loop tensioners are fed in, and the datum values relating to the lateral guides and to the thickness gauges are set up.

The rolling process continues in accordance with the remarks expressed following the principal claim, the process of the invention being limited to the determination of the datum values of the rolling mill train.

What is claimed is:

powers 1. Process for the predetermination of the datum values of a rolling mill finishing train for wide strip, controlled by a computer, wherein are imposed data such as: the thickness of the strip at the exit of the last frame of the rolling mill; the temperature of the strip at the exit of the rolling mill; and the required temperature of the strip at the coiler; wherein are specified: the nature of the steel of the strip; and the diameters of the working rolls; wherein measurements are made, such as: the

width of the strip; the temperature of the strip; and the thickness of the strip, these measurements being performed at the exit of the roughing pass train; and wherein by means of mathematical models, the speed of the strip at the exit from the rolling mill is determined; in which process the value of the profile of the strip at the exit of the rolling mill is specified; the process comprising the rollowing operations:

a. determining the instantaneous values of the curvature of the rolls, allowing for their wear and thermal condition;

b. determining the force to be applied to the last rollstand;

0. determining the thickness of the strip at the entrance to the last roll-stand;

d. selecting, on the basis of the characteristics of the strip to be rolled; the optimum distribution of power between the various roll-stands, and distributing the total power absorbed by the rolling mill accordingly;

e. checking that the power of each stand does not ex ceed a given maximum;

f. determining consecutively the thickness of the strip between the various roll-stands, the corresponding strip speeds, the peripheral speeds of the working rolls and the datum values of the angular speeds of the driving motors of these rolls;

g. calculating the forces exerted in the roll stands, and checking whether these forces exceed a given maximum value;

h. checking whether the distribution of forces renders it possible to produce a plane strip, and, if not, modifying the distribution of power between the stands;

. determining the datum values of the rolling mill train, of the position of the clamping screws, and of the forces at the automatic gauge control devices;

j. selecting the datum values for the loop tensioners;

and

k. feeding all the said datum values into corresponding servomechanisms operatively associated with the rolling mill train.

2. A process as claimed in claim 1, wherein the oper' ation (h) of checking the distribution of forces comprises calculating the profiles of the strip at the exit of the frames, calculating the planeity coefficient of each roll stand, and comparing the planeity coefficient with a given critical maximum value.

3. A process as claimed in claim 1, wherein the operation (c) of determining the thickness of the strip at the entrance to the last roll-stand, is followed by the consecutive operations of:

i. selecting the distribution of the forces to be applied to the stands;

ii. determining the forces to be applied to all the rollstands of the rolling mill train, except for the last roll-stand, and checking whether these forces exceed a given maximum value;

iii. determining the thicknesses of the strip;

iv. determining the datum values of the positions of the clamping screws;

v. feeding the datum values of the clamping screw positions and of the forces applied to the stands, into corresponding servomechanisms;

vi. determining of the profiles of the strip between the various roll-stands;

vii. deterrning the planeity coefficients and the critical values of these coefficients, and comparing them;

viii. if any of the planeity coefficients are above the corresponding critical value, introducing two kinds of correction into the computer memory unit, one applicable to the thickness of the strip, and the other applicable to the forces applied, to modify the selected distribution of the forces applied to the stands, until all the planeity coefficients are smaller than their respective critical values;

ix. determining the thickness reductions, the linear speeds of the strip, the slipping of the strip, and the circumferential speeds of the working rolls;

x. feeding the datum values of the speeds of the motors to corresponding servomechanisms.

xi. deterrning the power absorbed by each roll-stand and checking whether these powers remain smaller than a given maximum value; and

xii. feeding datum values to the loop tensioners, the

lateral guides, and the thickness gauges.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. Dated June 28, 1974 I lnventofls) Mario Economopoulos, et a].

It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

[73] Assignment:

Centre de Recherches Metallurgiques-Centrum voor Research in de Metallmc'gie Brussels, Belgium Signed and sealed this 4th day of March 1975.

(SEAL) Attest:

C. MARSHALL DANN RUTH C. MASON Commissioner of Patents Attesting Officer and Trademarks US COMM'DC 60376-P69 w uts. GOVERNMENT PRINTING OFFICE as" o--sse-3a4.

F ORM PO-1050 (10-69) 

1. Process for the predetermination of the datum values of a rolling mill finishing train for wide strip, controlled by a computer, wherein are imposed data such as: the thickness of the strip at the exit of the last frame of the rolling mill; the temperature of the strip at the exit of the rolling mill; and the required temperature of the strip at the coiler; wherein are specified: the nature of the steel of the strip; and the diameters of the working rolls; wherein measurements are made, such as: the width of the strip; the temperature of the strip; and the thickness of the strip, these measurements being performed at the exit of the roughing pass train; and wherein by means of mathematical models, the speed of the strip at the exit from the rolling mill is determined; in which process the value of the profile of the strip at the exit of the rolling mill is specified; the process comprising the rollowing operations: a. determining the instantaneous values of the curvature of the rolls, allowing for their wear and thermal Condition; b. determining the force to be applied to the last roll-stand; c. determining the thickness of the strip at the entrance to the last roll-stand; d. selecting, on the basis of the characteristics of the strip to be rolled; the optimum distribution of power between the various roll-stands, and distributing the total power absorbed by the rolling mill accordingly; e. checking that the power of each stand does not exceed a given maximum; f. determining consecutively the thickness of the strip between the various roll-stands, the corresponding strip speeds, the peripheral speeds of the working rolls and the datum values of the angular speeds of the driving motors of these rolls; g. calculating the forces exerted in the roll stands, and checking whether these forces exceed a given maximum value; h. checking whether the distribution of forces renders it possible to produce a plane strip, and, if not, modifying the distribution of power between the stands; i. determining the datum values of the rolling mill train, of the position of the clamping screws, and of the forces at the automatic gauge control devices; j. selecting the datum values for the loop tensioners; and k. feeding all the said datum values into corresponding servomechanisms operatively associated with the rolling mill train.
 2. A process as claimed in claim 1, wherein the operation (h) of checking the distribution of forces comprises calculating the profiles of the strip at the exit of the frames, calculating the planeity coefficient of each roll stand, and comparing the planeity coefficient with a given critical maximum value.
 3. A process as claimed in claim 1, wherein the operation (c) of determining the thickness of the strip at the entrance to the last roll-stand, is followed by the consecutive operations of: i. selecting the distribution of the forces to be applied to the stands; ii. determining the forces to be applied to all the roll-stands of the rolling mill train, except for the last roll-stand, and checking whether these forces exceed a given maximum value; iii. determining the thicknesses of the strip; iv. determining the datum values of the positions of the clamping screws; v. feeding the datum values of the clamping screw positions and of the forces applied to the stands, into corresponding servomechanisms; vi. determining of the profiles of the strip between the various roll-stands; vii. determing the planeity coefficients and the critical values of these coefficients, and comparing them; viii. if any of the planeity coefficients are above the corresponding critical value, introducing two kinds of correction into the computer memory unit, one applicable to the thickness of the strip, and the other applicable to the forces applied, to modify the selected distribution of the forces applied to the stands, until all the planeity coefficients are smaller than their respective critical values; ix. determining the thickness reductions, the linear speeds of the strip, the slipping of the strip, and the circumferential speeds of the working rolls; x. feeding the datum values of the speeds of the motors to corresponding servomechanisms. xi. determing the power absorbed by each roll-stand and checking whether these powers remain smaller than a given maximum value; and xii. feeding datum values to the loop tensioners, the lateral guides, and the thickness gauges. 